Preface to the Second Edition ................................ xiii
About the Author ............................................. xvii
List of Figures ............................................... xix
1 Down to Basics: Runoff Processes and the Modelling Process ... 1
1.1 Why Model? .............................................. 1
1.2 How to Use This Book .................................... 3
1.3 The Modelling Process ................................... 3
1.4 Perceptual Models of Catchment Hydrology ................ 6
1.5 Flow Processes and Geochemical Characteristics ......... 13
1.6 Runoff Generation and Runoff Routing ................... 15
1.7 The Problem of Choosing a Conceptual Model ............. 16
1.8 Model Calibration and Validation Issues ................ 18
1.9 Key Points from Chapter 1 .............................. 21
Box 1.1 The Legacy of Robert Elmer Horton (1875-1945) ...... 22
2 Evolution of Rainfall-Runoff Models: Survival of the
Fittest? .................................................... 25
2.1 The Starting Point: The Rational Method ................ 25
2.2 Practical Prediction: Runoff Coefficients and Time
Transformations ........................................ 26
2.3 Variations on the Unit Hydrograph ...................... 33
2.4 Early Digital Computer Models: The Stanford Watershed
Model and Its Descendants .............................. 36
2.5 Distributed Process Description Based Models ........... 40
2.6 Simplified Distributed Models Based on Distribution
Functions .............................................. 42
2.7 Recent Developments: What is the Current State of the
Art? ................................................... 43
2.8 Where to Find More on the History and Variety of
Rainfall-Runoff Models ................................. 43
2.9 Key Points from Chapter 2 .............................. 44
Box 2.1 Linearity, Nonlinearity and Nonstationarity ......... 45
Box 2.2 The Xinanjiang, ARNO or VIC Model ................... 46
Box 2.3 Control Volumes and Differential Equations .......... 49
3 Data for Rainfall-Runoff Modelling .......................... 51
3.1 Rainfall Data .......................................... 51
3.2 Discharge Data ......................................... 55
3.3 Meteorological Data and the Estimation of
Interception and Evapotranspiration .................... 56
3.4 Meteorological Data and The Estimation of Snowmelt ..... 60
3.5 Distributing Meteorological Data within a Catchment .... 61
3.6 Other Hydrological Variables ........................... 61
3.7 Digital Elevation Data ................................. 61
3.8 Geographical Information and Data Management Systems ... 66
3.9 Remote-sensing Data .................................... 67
3.10 Tracer Data for Understanding Catchment Responses ...... 69
3.11 Linking Model Components and Data Series ............... 70
3.12 Key Points from Chapter 3 .............................. 71
Box 3.1 The Penman-Monteith Combination Equation for
Estimating Evapotranspiration Rates ................. 72
Box 3.2 Estimating Interception Losses ...................... 76
Box 3.3 Estimating Snowmelt by the Degree-Day Method ........ 79
4 Predicting Hydrographs Using Models Based on Data ........... 83
4.1 Data Availability and Empirical Modelling .............. 83
4.2 Doing Hydrology Backwards .............................. 84
4.3 Transfer Function Models ............................... 87
4.4 Case Study: DBM Modelling of the CI6 Catchment at
Llyn Briane, Wales ..................................... 93
4.5 Physical Derivation of Transfer Functions .............. 95
4.6 Other Methods of Developing Inductive Rainfall-Runoff
Models from Observations ............................... 99
4.7 Key Points from Chapter 4 ............................. 106
Box 4.1 Linear Transfer Function Models .................... 107
Box 4.2 Use of Transfer Functions to Infer Effective
Rainfalls .......................................... 112
Box 4.3 Time Variable Estimation of Transfer Function
Parameters and Derivation of Catchment
Nonlinearity ....................................... 113
5 Predicting Hydrographs Using Distributed Models Based on
Process Descriptions ....................................... 119
5.1 The Physical Basis of Distributed Models .............. 119
5.2 Physically Based Rainfall-Runoff Models at the
Catchment Scale ....................................... 128
5.3 Case Study: Modelling Flow Processes at Reynolds
Creek, Idaho .......................................... 135
5.4 Case Study: Blind Validation Test of the SHE Model
on the Slapton Wood Catchment ......................... 138
5.5 Simplified Distributed Models ......................... 140
5.6 Case Study: Distributed Modelling of Runoff
Generation at Walnut Gulch, Arizona ................... 148
5.7 Case Study: Modelling the R-5 Catchment at
Chickasha, Oklahoma ................................... 151
5.8 Good Practice in the Application of Distributed
Models ................................................ 154
5.9 Discussion of Distributed Models Based on Continuum
Differential Equations ................................ 155
5.10 Key Points from Chapter 5 ............................. 157
Box 5.1 Descriptive Equations for Subsurface Flows ......... 158
Box 5.2 Estimating Infiltration Rates at the Soil Surface .. 160
Box 5.3 Solution of Partial Differential Equations: Some
Basic Concepts ..................................... 166
Box 5.4 Soil Moisture Characteristic Functions for Use in
the Richards Equation .............................. 171
Box 5.5 Pedotransfer Functions ............................. 175
Box 5.6 Descriptive Equations for Surface Flows ............ 177
Box 5.7 Derivation of the Kinematic Wave Equation .......... 181
6 Hydrological Similarity, Distribution Functions and Semi-
Distributed Rainfall-Runoff Models ......................... 185
6.1 Hydrological Similarity and Hydrological Response
Units ................................................. 185
6.2 The Probability Distributed Moisture (PDM) and Grid
to Grid (G2G) Models .................................. 187
6.3 TOPMODEL .............................................. 190
6.4 Case Study: Application of TOPMODEL to the
Saeternbekken Catchment, Norway ....................... 198
6.5 TOPKAPI ............................................... 203
6.6 Semi-Distributed Hydrological Response Unit (HRU)
Models ................................................ 204
6.7 Some Comments on the HRU Approach ..................... 207
6.8 Key Points from Chapter 6 ............................. 208
Box 6.1 The Theory Underlying TOPMODEL ..................... 210
Box 6.2 The Soil and Water Assessment Tool (SWAT) Model .... 219
Box 6.3 The SCS Curve Number Model Revisited ............... 224
7 Parameter Estimation and Predictive Uncertainty ............ 231
7.1 Model Calibration or Conditioning ..................... 231
7.2 Parameter Response Surfaces and Sensitivity Analysis .. 233
7.3 Performance Measures and Likelihood Measures .......... 239
7.4 Automatic Optimisation Techniques ..................... 241
7.5 Recognising Uncertainty in Models and Data: Forward
Uncertainty Estimation ................................ 243
7.6 Types of Uncertainty Interval ......................... 244
7.7 Model Calibration Using Bayesian Statistical Methods .. 245
7.8 Dealing with Input Uncertainty in a Bayesian
Framework ............................................. 247
7.9 Model Calibration Using Set Theoretic Methods ......... 249
7.10 Recognising Equifinality: The GLUE Method ............. 252
7.11 Case Study: An Application of the GLUE Methodology
in Modelling the Saeternbekken MINIFELT Catchment,
Norway ................................................ 258
7.12 Case Study: Application of GLUE Limits of
Acceptability Approach to Evaluation in Modelling
the Brue Catchment, Somerset, England ................. 261
7.13 Other Applications of GLUE in Rainfall-Runoff
Modelling ............................................. 265
7.14 Comparison of GLUE and Bayesian Approaches to
Uncertainty Estimation ................................ 266
7.15 Predictive Uncertainty, Risk and Decisions ............ 267
7.16 Dynamic Parameters and Model Structural Error ......... 268
7.17 Quality Control and Disinformation in Rainfall-
Runoff Modelling ...................................... 269
7.18 The Value of Data in Model Conditioning ............... 274
7.19 Key Points from Chapter 7 ............................. 274
Box 7.1 Likelihood Measures for use in Evaluating Models ... 276
Box 7.2 Combining Likelihood Measures ...................... 283
Box 7.3 Defining the Shape of a Response or Likelihood
Surface ............................................ 284
8 Beyond the Primer: Models for Changing Risk ................ 289
8.1 The Role of Rainfall-Runoff Models in Managing
Future Risk ........................................... 289
8.2 Short-Term Future Risk: Flood Forecasting ............. 290
8.3 Data Requirements for Flood Forecasting ............... 291
8.4 Rainfall-Runoff Modelling for Flood Forecasting ....... 293
8.5 Case Study: Flood Forecasting in the River Eden
Catchment, Cumbria, England ........................... 297
8.6 Rainfall-Runoff Modelling for Flood Frequency
Estimation ............................................ 299
8.7 Case Study: Modelling the Flood Frequency
Characteristics on the Skalka Catchment, Czech
Republic .............................................. 302
8.8 Changing Risk: Catchment Change ....................... 305
8.9 Changing Risk: Climate Change ......................... 307
8.10 Key Points from Chapter 8 ............................. 309
Box 8.1 Adaptive Gain Parameter Estimation for Real-Time
Forecasting ........................................ 311
9 Beyond the Primer: Next Generation Hydrological Models ..... 313
9.1 Why are New Modelling Techniques Needed? .............. 313
9.2 Representative Elementary Watershed Concepts .......... 315
9.3 How are the REW Concepts Different from Other
Hydrological Models? .................................. 318
9.4 Implementation of the REW Concepts .................... 318
9.5 Inferring Scale-Dependent Hysteresis from Simplified
Hydrological Theory ................................... 320
9.6 Representing Water Fluxes by Particle Tracking ........ 321
9.7 Catchments as Complex Adaptive Systems ................ 324
9.8 Optimality Constraints on Hydrological Responses ...... 325
9.9 Key Points from Chapter 9 ............................. 327
10 Beyond the Primer: Predictions in Ungauged Basins .......... 329
10.1 The Ungauged Catchment Challenge ...................... 329
10.2 The PUB Initiative .................................... 330
10.3 The MOPEX Initiative .................................. 331
10.4 Ways of Making Predictions in Ungauged Basins ......... 331
10.5 PUB as a Learning Process ............................. 332
10.6 Regression of Model Parameters Against Catchment
Characteristics ....................................... 333
10.7 Donor Catchment and Pooling Group Methods ............. 335
10.8 Direct Estimation of Hydrograph Characteristics for
Constraining Model Parameters ......................... 336
10.9 Comparing Regionalisation Methods for Model
Parameters ............................................ 338
10.10 HRUs and LSPs as Models of Ungauged Basins ........... 339
10.11 Gauging the Ungauged Basin ........................... 339
10.12 Key Points from Chapter 10 ........................... 341
11 Beyond the Primer: Water Sources and Residence Times in
Catchments ................................................. 343
11.1 Natural and Artificial Tracers ........................ 343
11.2 Advection and Dispersion in the Catchment System ...... 345
11.3 Simple Mixing Models .................................. 346
11.4 Assessing Spatial Patterns of Incremental Discharge ... 347
11.5 End Member Mixing Analysis (EMMA) ..................... 347
11.6 On the Implications of Tracer Information for
Hydrological Processes ................................ 348
11.7 Case Study: End Member Mixing with Routing ............ 349
11.8 Residence Time Distribution Models .................... 353
11.9 Case Study: Predicting Tracer Transport at the
Gårdsjön Catchment, Sweden ............................ 357
11.10 Implications for Water Quality Models ................ 359
11.11 Key Points from Chapter 11 ........................... 360
Box 11.1 Representing Advection and Dispersion ............. 361
Box 11.2 Analysing Residence Times in Catchment Systems .... 365
12 Beyond the Primer: Hypotheses, Measurements and Models of
Everywhere ................................................. 369
12.1 Model Choice in Rainfall-Runoff Modelling as
Hypothesis Testing .................................... 369
12.2 The Value of Prior Information ........................ 371
12.3 Models as Hypotheses .................................. 372
12.4 Models of Everywhere .................................. 374
12.5 Guidelines for Good Practice .......................... 375
12.6 Models of Everywhere and Stakeholder Involvement ...... 376
12.7 Models of Every where and Information ................. 377
12.8 Some Final Questions .................................. 378
Appendix A Web Resources for Software and Data ................ 381
Appendix В Glossary of Terms .................................. 387
References .................................................... 397
Index ......................................................... 449
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